LMFDB - Embedded newform 882.4.g.bj.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-3.22311 - 5.58259i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.bj.667.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.22311 + 9.04669i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.22311 + 9.04669i) q^{5} -8.00000 q^{8} +(-10.4462 + 18.0934i) q^{10} +(30.5618 - 52.9346i) q^{11} +59.2311 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-10.2311 + 17.7208i) q^{17} +(-40.1693 - 69.5753i) q^{19} -41.7849 q^{20} +122.247 q^{22} +(-79.1236 - 137.046i) q^{23} +(7.93822 - 13.7494i) q^{25} +(59.2311 + 102.591i) q^{26} +85.1236 q^{29} +(121.747 - 210.872i) q^{31} +(16.0000 - 27.7128i) q^{32} -40.9244 q^{34} +(-145.185 - 251.468i) q^{37} +(80.3387 - 139.151i) q^{38} +(-41.7849 - 72.3735i) q^{40} -168.000 q^{41} +7.62934 q^{43} +(122.247 + 211.738i) q^{44} +(158.247 - 274.092i) q^{46} +(84.6453 + 146.610i) q^{47} +31.7529 q^{50} +(-118.462 + 205.183i) q^{52} +(-125.056 + 216.603i) q^{53} +638.510 q^{55} +(85.1236 + 147.438i) q^{58} +(402.610 - 697.341i) q^{59} +(16.5858 + 28.7274i) q^{61} +486.988 q^{62} +64.0000 q^{64} +(309.371 + 535.846i) q^{65} +(138.691 - 240.220i) q^{67} +(-40.9244 - 70.8832i) q^{68} +631.506 q^{71} +(-384.142 + 665.353i) q^{73} +(290.371 - 502.937i) q^{74} +321.355 q^{76} +(209.365 + 362.631i) q^{79} +(83.5698 - 144.747i) q^{80} +(-168.000 - 290.985i) q^{82} -761.714 q^{83} -213.753 q^{85} +(7.62934 + 13.2144i) q^{86} +(-244.494 + 423.476i) q^{88} +(786.048 + 1361.48i) q^{89} +632.988 q^{92} +(-169.291 + 293.220i) q^{94} +(419.618 - 726.799i) q^{95} -1045.16 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8} - 14 q^{10} + 25 q^{11} + 98 q^{13} - 32 q^{16} + 98 q^{17} - 119 q^{19} - 56 q^{20} + 100 q^{22} - 122 q^{23} + 129 q^{25} + 98 q^{26} + 146 q^{29} + 98 q^{31} + 64 q^{32} + 392 q^{34} - 289 q^{37} + 238 q^{38} - 56 q^{40} - 672 q^{41} + 614 q^{43} + 100 q^{44} + 244 q^{46} + 672 q^{47} + 516 q^{50} - 196 q^{52} + 375 q^{53} + 1526 q^{55} + 146 q^{58} + 763 q^{59} - 406 q^{61} + 392 q^{62} + 256 q^{64} + 654 q^{65} + 1041 q^{67} + 392 q^{68} + 3304 q^{71} - 189 q^{73} + 578 q^{74} + 952 q^{76} - 524 q^{79} + 112 q^{80} - 672 q^{82} - 574 q^{83} - 1244 q^{85} + 614 q^{86} - 200 q^{88} + 2394 q^{89} + 976 q^{92} - 1344 q^{94} + 706 q^{95} + 126 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8 - 14 * q^10 + 25 * q^11 + 98 * q^13 - 32 * q^16 + 98 * q^17 - 119 * q^19 - 56 * q^20 + 100 * q^22 - 122 * q^23 + 129 * q^25 + 98 * q^26 + 146 * q^29 + 98 * q^31 + 64 * q^32 + 392 * q^34 - 289 * q^37 + 238 * q^38 - 56 * q^40 - 672 * q^41 + 614 * q^43 + 100 * q^44 + 244 * q^46 + 672 * q^47 + 516 * q^50 - 196 * q^52 + 375 * q^53 + 1526 * q^55 + 146 * q^58 + 763 * q^59 - 406 * q^61 + 392 * q^62 + 256 * q^64 + 654 * q^65 + 1041 * q^67 + 392 * q^68 + 3304 * q^71 - 189 * q^73 + 578 * q^74 + 952 * q^76 - 524 * q^79 + 112 * q^80 - 672 * q^82 - 574 * q^83 - 1244 * q^85 + 614 * q^86 - 200 * q^88 + 2394 * q^89 + 976 * q^92 - 1344 * q^94 + 706 * q^95 + 126 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	5.22311	+	9.04669i	0.467169	+	0.809161i	0.999296	−	0.0375035i	$-0.0119405\pi$
$5$	5.22311	+	9.04669i	0.467169	+	0.809161i	−0.532127	+	0.846664i	$0.678607\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−10.4462	+	18.0934i	−0.330339	+	0.572163i
$11$	30.5618	−	52.9346i	0.837702	−	1.45094i	−0.0541093	−	0.998535i	$-0.517232\pi$
$11$	30.5618	−	52.9346i	0.837702	−	1.45094i	0.891811	−	0.452407i	$-0.149435\pi$
$12$		0			0
$13$	59.2311			1.26367			0.631837	−	0.775102i	$-0.282301\pi$
$13$	59.2311			1.26367			0.631837	+	0.775102i	$0.282301\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−10.2311	+	17.7208i	−0.145965	+	0.252819i	−0.929733	−	0.368235i	$-0.879962\pi$
$17$	−10.2311	+	17.7208i	−0.145965	+	0.252819i	0.783767	+	0.621054i	$0.213295\pi$
$18$		0			0
$19$	−40.1693	−	69.5753i	−0.485025	−	0.840088i	0.514827	−	0.857294i	$-0.327856\pi$
$19$	−40.1693	−	69.5753i	−0.485025	−	0.840088i	−0.999852	+	0.0172061i	$0.994523\pi$
$20$	−41.7849			−0.467169
$21$		0			0
$22$	122.247			1.18469
$23$	−79.1236	−	137.046i	−0.717322	−	1.24244i	−0.962057	−	0.272848i	$-0.912034\pi$
$23$	−79.1236	−	137.046i	−0.717322	−	1.24244i	0.244735	−	0.969590i	$-0.421299\pi$
$24$		0			0
$25$	7.93822	−	13.7494i	0.0635058	−	0.109995i
$26$	59.2311	+	102.591i	0.446776	+	0.773839i
$27$		0			0
$28$		0			0
$29$	85.1236			0.545071			0.272535	−	0.962146i	$-0.412138\pi$
$29$	85.1236			0.545071			0.272535	+	0.962146i	$0.412138\pi$
$30$		0			0
$31$	121.747	−	210.872i	0.705369	−	1.22173i	−0.261190	−	0.965287i	$-0.584115\pi$
$31$	121.747	−	210.872i	0.705369	−	1.22173i	0.966558	−	0.256447i	$-0.0825518\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−40.9244			−0.206426
$35$		0			0
$36$		0			0
$37$	−145.185	−	251.468i	−0.645090	−	1.11733i	−0.984281	−	0.176611i	$-0.943487\pi$
$37$	−145.185	−	251.468i	−0.645090	−	1.11733i	0.339191	−	0.940718i	$-0.389847\pi$
$38$	80.3387	−	139.151i	0.342965	−	0.594032i
$39$		0			0
$40$	−41.7849	−	72.3735i	−0.165169	−	0.286082i
$41$	−168.000			−0.639932			−0.319966	−	0.947429i	$-0.603671\pi$
$41$	−168.000			−0.639932			−0.319966	+	0.947429i	$0.603671\pi$
$42$		0			0
$43$	7.62934			0.0270573			0.0135286	−	0.999908i	$-0.495694\pi$
$43$	7.62934			0.0270573			0.0135286	+	0.999908i	$0.495694\pi$
$44$	122.247	+	211.738i	0.418851	+	0.725471i
$45$		0			0
$46$	158.247	−	274.092i	0.507223	−	0.878536i
$47$	84.6453	+	146.610i	0.262698	+	0.455006i	0.966958	−	0.254936i	$-0.0820545\pi$
$47$	84.6453	+	146.610i	0.262698	+	0.455006i	−0.704260	+	0.709942i	$0.748721\pi$
$48$		0			0
$49$		0			0
$50$	31.7529			0.0898107
$51$		0			0
$52$	−118.462	+	205.183i	−0.315918	+	0.547187i
$53$	−125.056	+	216.603i	−0.324109	+	0.561373i	−0.981332	−	0.192324i	$-0.938398\pi$
$53$	−125.056	+	216.603i	−0.324109	+	0.561373i	0.657223	+	0.753696i	$0.271731\pi$
$54$		0			0
$55$	638.510			1.56539
$56$		0			0
$57$		0			0
$58$	85.1236	+	147.438i	0.192712	+	0.333786i
$59$	402.610	−	697.341i	0.888395	−	1.53875i	0.0466235	−	0.998913i	$-0.485154\pi$
$59$	402.610	−	697.341i	0.888395	−	1.53875i	0.841772	−	0.539833i	$-0.181513\pi$
$60$		0			0
$61$	16.5858	+	28.7274i	0.0348130	+	0.0602978i	0.882907	−	0.469548i	$-0.155583\pi$
$61$	16.5858	+	28.7274i	0.0348130	+	0.0602978i	−0.848094	+	0.529846i	$0.822250\pi$
$62$	486.988			0.997542
$63$		0			0
$64$	64.0000			0.125000
$65$	309.371	+	535.846i	0.590349	+	1.02252i
$66$		0			0
$67$	138.691	−	240.220i	0.252893	−	0.438023i	−0.711428	−	0.702759i	$-0.751951\pi$
$67$	138.691	−	240.220i	0.252893	−	0.438023i	0.964321	+	0.264736i	$0.0852847\pi$
$68$	−40.9244	−	70.8832i	−0.0729826	−	0.126410i
$69$		0			0
$70$		0			0
$71$	631.506			1.05558			0.527788	−	0.849376i	$-0.323021\pi$
$71$	631.506			1.05558			0.527788	+	0.849376i	$0.323021\pi$
$72$		0			0
$73$	−384.142	+	665.353i	−0.615896	+	1.06676i	0.374331	+	0.927295i	$0.377872\pi$
$73$	−384.142	+	665.353i	−0.615896	+	1.06676i	−0.990227	+	0.139468i	$0.955461\pi$
$74$	290.371	−	502.937i	0.456147	−	0.790070i
$75$		0			0
$76$	321.355			0.485025
$77$		0			0
$78$		0			0
$79$	209.365	+	362.631i	0.298169	+	0.516445i	0.975717	−	0.219034i	$-0.0702906\pi$
$79$	209.365	+	362.631i	0.298169	+	0.516445i	−0.677548	+	0.735479i	$0.736957\pi$
$80$	83.5698	−	144.747i	0.116792	−	0.202290i
$81$		0			0
$82$	−168.000	−	290.985i	−0.226250	−	0.391876i
$83$	−761.714			−1.00734			−0.503668	−	0.863897i	$-0.668017\pi$
$83$	−761.714			−1.00734			−0.503668	+	0.863897i	$0.668017\pi$
$84$		0			0
$85$	−213.753			−0.272762
$86$	7.62934	+	13.2144i	0.00956619	+	0.0165691i
$87$		0			0
$88$	−244.494	+	423.476i	−0.296172	+	0.512986i
$89$	786.048	+	1361.48i	0.936190	+	1.62153i	0.772498	+	0.635017i	$0.219007\pi$
$89$	786.048	+	1361.48i	0.936190	+	1.62153i	0.163692	+	0.986511i	$0.447660\pi$
$90$		0			0
$91$		0			0
$92$	632.988			0.717322
$93$		0			0
$94$	−169.291	+	293.220i	−0.185755	+	0.321738i
$95$	419.618	−	726.799i	0.453178	−	0.784927i
$96$		0			0
$97$	−1045.16			−1.09402			−0.547012	−	0.837125i	$-0.684235\pi$
$97$	−1045.16			−1.09402			−0.547012	+	0.837125i	$0.684235\pi$
$98$		0			0
$99$		0			0
$100$	31.7529	+	54.9976i	0.0317529	+	0.0549976i
$101$	−487.961	+	845.173i	−0.480732	+	0.832652i	−0.999756	−	0.0221078i	$-0.992962\pi$
$101$	−487.961	+	845.173i	−0.480732	+	0.832652i	0.519024	+	0.854760i	$0.326296\pi$
$102$		0			0
$103$	−321.572	−	556.979i	−0.307626	−	0.532823i	0.670217	−	0.742165i	$-0.266201\pi$
$103$	−321.572	−	556.979i	−0.307626	−	0.532823i	−0.977842	+	0.209342i	$0.932868\pi$
$104$	−473.849			−0.446776
$105$		0			0
$106$	−500.224			−0.458359
$107$	−155.797	−	269.849i	−0.140762	−	0.243806i	0.787022	−	0.616925i	$-0.211622\pi$
$107$	−155.797	−	269.849i	−0.140762	−	0.243806i	−0.927784	+	0.373119i	$0.878288\pi$
$108$		0			0
$109$	932.915	−	1615.86i	0.819790	−	1.41992i	−0.0860476	−	0.996291i	$-0.527424\pi$
$109$	932.915	−	1615.86i	0.819790	−	1.41992i	0.905837	−	0.423626i	$-0.139243\pi$
$110$	638.510	+	1105.93i	0.553451	+	0.958604i
$111$		0			0
$112$		0			0
$113$	1720.49			1.43231			0.716153	−	0.697944i	$-0.245901\pi$
$113$	1720.49			1.43231			0.716153	+	0.697944i	$0.245901\pi$
$114$		0			0
$115$	826.542	−	1431.61i	0.670221	−	1.16086i
$116$	−170.247	+	294.877i	−0.136268	+	0.236022i
$117$		0			0
$118$	1610.44			1.25638
$119$		0			0
$120$		0			0
$121$	−1202.54	−	2082.87i	−0.903489	−	1.56489i
$122$	−33.1715	+	57.4548i	−0.0246165	+	0.0426370i
$123$		0			0
$124$	486.988	+	843.489i	0.352684	+	0.610867i
$125$	1471.63			1.05301
$126$		0			0
$127$	142.236			0.0993808			0.0496904	−	0.998765i	$-0.484177\pi$
$127$	142.236			0.0993808			0.0496904	+	0.998765i	$0.484177\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−618.741	+	1071.69i	−0.417440	+	0.723027i
$131$	1243.26	+	2153.38i	0.829189	+	1.43620i	0.898676	+	0.438614i	$0.144530\pi$
$131$	1243.26	+	2153.38i	0.829189	+	1.43620i	−0.0694870	+	0.997583i	$0.522136\pi$
$132$		0			0
$133$		0			0
$134$	554.764			0.357644
$135$		0			0
$136$	81.8489	−	141.766i	0.0516065	−	0.0893851i
$137$	1298.61	−	2249.25i	0.809835	−	1.40268i	−0.103143	−	0.994667i	$-0.532890\pi$
$137$	1298.61	−	2249.25i	0.809835	−	1.40268i	0.912978	−	0.408009i	$-0.133777\pi$
$138$		0			0
$139$	−1600.52			−0.976651			−0.488325	−	0.872662i	$-0.662392\pi$
$139$	−1600.52			−0.976651			−0.488325	+	0.872662i	$0.662392\pi$
$140$		0			0
$141$		0			0
$142$	631.506	+	1093.80i	0.373203	+	0.646406i
$143$	1810.21	−	3135.37i	1.05858	−	1.83352i
$144$		0			0
$145$	444.610	+	770.087i	0.254640	+	0.441050i
$146$	−1536.57			−0.871008
$147$		0			0
$148$	1161.48			0.645090
$149$	1468.85	+	2544.13i	0.807605	+	1.39881i	0.914518	+	0.404545i	$0.132570\pi$
$149$	1468.85	+	2544.13i	0.807605	+	1.39881i	−0.106913	+	0.994268i	$0.534097\pi$
$150$		0			0
$151$	−911.662	+	1579.05i	−0.491325	+	0.850999i	−0.999950	−	0.00998867i	$-0.996820\pi$
$151$	−911.662	+	1579.05i	−0.491325	+	0.850999i	0.508625	+	0.860988i	$0.330154\pi$
$152$	321.355	+	556.603i	0.171482	+	0.297016i
$153$		0			0
$154$		0			0
$155$	2543.59			1.31811
$156$		0			0
$157$	316.824	−	548.755i	0.161053	−	0.278952i	−0.774194	−	0.632949i	$-0.781844\pi$
$157$	316.824	−	548.755i	0.161053	−	0.278952i	0.935247	+	0.353997i	$0.115178\pi$
$158$	−418.730	+	725.261i	−0.210838	+	0.365182i
$159$		0			0
$160$	334.279			0.165169
$161$		0			0
$162$		0			0
$163$	672.853	+	1165.42i	0.323325	+	0.560015i	0.981172	−	0.193137i	$-0.0618660\pi$
$163$	672.853	+	1165.42i	0.323325	+	0.560015i	−0.657847	+	0.753151i	$0.728533\pi$
$164$	336.000	−	581.969i	0.159983	−	0.277098i
$165$		0			0
$166$	−761.714	−	1319.33i	−0.356147	−	0.616865i
$167$	387.922			0.179750			0.0898751	−	0.995953i	$-0.471353\pi$
$167$	387.922			0.179750			0.0898751	+	0.995953i	$0.471353\pi$
$168$		0			0
$169$	1311.32			0.596870
$170$	−213.753	−	370.231i	−0.0964359	−	0.167032i
$171$		0			0
$172$	−15.2587	+	26.4288i	−0.00676432	+	0.0117161i
$173$	311.330	+	539.239i	0.136821	+	0.236980i	0.926291	−	0.376808i	$-0.122978\pi$
$173$	311.330	+	539.239i	0.136821	+	0.236980i	−0.789471	+	0.613788i	$0.789645\pi$
$174$		0			0
$175$		0			0
$176$	−977.977			−0.418851
$177$		0			0
$178$	−1572.10	+	2722.95i	−0.661986	+	1.14659i
$179$	−224.965	+	389.651i	−0.0939368	+	0.162703i	−0.909164	−	0.416437i	$-0.863279\pi$
$179$	−224.965	+	389.651i	−0.0939368	+	0.162703i	0.815228	+	0.579141i	$0.196612\pi$
$180$		0			0
$181$	−184.353			−0.0757063			−0.0378532	−	0.999283i	$-0.512052\pi$
$181$	−184.353			−0.0757063			−0.0378532	+	0.999283i	$0.512052\pi$
$182$		0			0
$183$		0			0
$184$	632.988	+	1096.37i	0.253612	+	0.439268i
$185$	1516.64	−	2626.89i	0.602732	−	1.04396i
$186$		0			0
$187$	625.362	+	1083.16i	0.244551	+	0.423574i
$188$	−677.163			−0.262698
$189$		0			0
$190$	1678.47			0.640890
$191$	175.483	+	303.945i	0.0664789	+	0.115145i	0.897349	−	0.441321i	$-0.145490\pi$
$191$	175.483	+	303.945i	0.0664789	+	0.115145i	−0.830870	+	0.556466i	$0.812157\pi$
$192$		0			0
$193$	−764.129	+	1323.51i	−0.284991	+	0.493619i	−0.972607	−	0.232456i	$-0.925324\pi$
$193$	−764.129	+	1323.51i	−0.284991	+	0.493619i	0.687616	+	0.726074i	$0.258657\pi$
$194$	−1045.16	−	1810.28i	−0.386796	−	0.669950i
$195$		0			0
$196$		0			0
$197$	−2874.65			−1.03965			−0.519823	−	0.854274i	$-0.674002\pi$
$197$	−2874.65			−1.03965			−0.519823	+	0.854274i	$0.674002\pi$
$198$		0			0
$199$	2474.35	−	4285.70i	0.881418	−	1.52666i	0.0316529	−	0.999499i	$-0.489923\pi$
$199$	2474.35	−	4285.70i	0.881418	−	1.52666i	0.849765	−	0.527162i	$-0.176744\pi$
$200$	−63.5058	+	109.995i	−0.0224527	+	0.0388892i
$201$		0			0
$202$	−1951.84			−0.679858
$203$		0			0
$204$		0			0
$205$	−877.483	−	1519.84i	−0.298956	−	0.517808i
$206$	643.144	−	1113.96i	0.217524	−	0.376763i
$207$		0			0
$208$	−473.849	−	820.730i	−0.157959	−	0.273593i
$209$	−4910.58			−1.62523
$210$		0			0
$211$	−5280.90			−1.72299			−0.861497	−	0.507762i	$-0.830473\pi$
$211$	−5280.90			−1.72299			−0.861497	+	0.507762i	$0.830473\pi$
$212$	−500.224	−	866.413i	−0.162054	−	0.280686i
$213$		0			0
$214$	311.595	−	539.698i	0.0995335	−	0.172397i
$215$	39.8489	+	69.0203i	0.0126403	+	0.0218937i
$216$		0			0
$217$		0			0
$218$	3731.66			1.15936
$219$		0			0
$220$	−1277.02	+	2211.86i	−0.391349	+	0.677836i
$221$	−606.000	+	1049.62i	−0.184452	+	0.319481i
$222$		0			0
$223$	−3996.57			−1.20013			−0.600067	−	0.799950i	$-0.704859\pi$
$223$	−3996.57			−1.20013			−0.600067	+	0.799950i	$0.704859\pi$
$224$		0			0
$225$		0			0
$226$	1720.49	+	2979.98i	0.506396	+	0.877104i
$227$	−269.296	+	466.434i	−0.0787392	+	0.136380i	−0.902706	−	0.430257i	$-0.858423\pi$
$227$	−269.296	+	466.434i	−0.0787392	+	0.136380i	0.823967	+	0.566638i	$0.191756\pi$
$228$		0			0
$229$	2085.80	+	3612.72i	0.601895	+	1.04251i	0.992534	+	0.121968i	$0.0389206\pi$
$229$	2085.80	+	3612.72i	0.601895	+	1.04251i	−0.390639	+	0.920544i	$0.627746\pi$
$230$	3306.17			0.947836
$231$		0			0
$232$	−680.988			−0.192712
$233$	−769.865	−	1333.45i	−0.216461	−	0.374922i	0.737262	−	0.675607i	$-0.236118\pi$
$233$	−769.865	−	1333.45i	−0.216461	−	0.374922i	−0.953724	+	0.300684i	$0.902785\pi$
$234$		0			0
$235$	−884.224	+	1531.52i	−0.245449	+	0.425129i
$236$	1610.44	+	2789.36i	0.444198	+	0.769373i
$237$		0			0
$238$		0			0
$239$	3132.67			0.847848			0.423924	−	0.905698i	$-0.360652\pi$
$239$	3132.67			0.847848			0.423924	+	0.905698i	$0.360652\pi$
$240$		0			0
$241$	1303.35	−	2257.46i	0.348365	−	0.603386i	−0.637594	−	0.770372i	$-0.720070\pi$
$241$	1303.35	−	2257.46i	0.348365	−	0.603386i	0.985959	+	0.166987i	$0.0534037\pi$
$242$	2405.09	−	4165.74i	0.638863	−	1.10654i
$243$		0			0
$244$	−132.686			−0.0348130
$245$		0			0
$246$		0			0
$247$	−2379.27	−	4121.02i	−0.612913	−	1.06160i
$248$	−973.977	+	1686.98i	−0.249385	+	0.431948i
$249$		0			0
$250$	1471.63	+	2548.93i	0.372295	+	0.644834i
$251$	3426.24			0.861603			0.430801	−	0.902447i	$-0.358231\pi$
$251$	3426.24			0.861603			0.430801	+	0.902447i	$0.358231\pi$
$252$		0			0
$253$	−9672.63			−2.40361
$254$	142.236	+	246.359i	0.0351364	+	0.0608581i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2928.72	+	5072.69i	0.710850	+	1.23123i	0.964538	+	0.263943i	$0.0850230\pi$
$257$	2928.72	+	5072.69i	0.710850	+	1.23123i	−0.253688	+	0.967286i	$0.581644\pi$
$258$		0			0
$259$		0			0
$260$	−2474.97			−0.590349
$261$		0			0
$262$	−2486.51	+	4306.76i	−0.586325	+	1.01554i
$263$	542.965	−	940.443i	0.127303	−	0.220495i	−0.795328	−	0.606180i	$-0.792701\pi$
$263$	542.965	−	940.443i	0.127303	−	0.220495i	0.922631	+	0.385684i	$0.126035\pi$
$264$		0			0
$265$	−2612.73			−0.605654
$266$		0			0
$267$		0			0
$268$	554.764	+	960.880i	0.126446	+	0.219012i
$269$	−2789.73	+	4831.95i	−0.632315	+	1.09520i	0.354763	+	0.934956i	$0.384562\pi$
$269$	−2789.73	+	4831.95i	−0.632315	+	1.09520i	−0.987077	+	0.160245i	$0.948772\pi$
$270$		0			0
$271$	−280.164	−	485.258i	−0.0627997	−	0.108772i	0.832916	−	0.553399i	$-0.186670\pi$
$271$	−280.164	−	485.258i	−0.0627997	−	0.108772i	−0.895716	+	0.444627i	$0.853336\pi$
$272$	327.396			0.0729826
$273$		0			0
$274$	5194.42			1.14528
$275$	−485.212	−	840.413i	−0.106398	−	0.184286i
$276$		0			0
$277$	2254.04	−	3904.11i	0.488924	−	0.846842i	−0.510994	−	0.859584i	$-0.670723\pi$
$277$	2254.04	−	3904.11i	0.488924	−	0.846842i	0.999919	+	0.0127421i	$0.00405606\pi$
$278$	−1600.52	−	2772.19i	−0.345298	−	0.598074i
$279$		0			0
$280$		0			0
$281$	−4329.75			−0.919186			−0.459593	−	0.888130i	$-0.652005\pi$
$281$	−4329.75			−0.919186			−0.459593	+	0.888130i	$0.652005\pi$
$282$		0			0
$283$	−435.526	+	754.353i	−0.0914817	+	0.158451i	−0.908135	−	0.418678i	$-0.862494\pi$
$283$	−435.526	+	754.353i	−0.0914817	+	0.158451i	0.816653	+	0.577129i	$0.195827\pi$
$284$	−1263.01	+	2187.60i	−0.263894	+	0.457078i
$285$		0			0
$286$	7240.83			1.49706
$287$		0			0
$288$		0			0
$289$	2247.15	+	3892.18i	0.457388	+	0.792220i
$290$	−889.220	+	1540.17i	−0.180058	+	0.311869i
$291$		0			0
$292$	−1536.57	−	2661.41i	−0.307948	−	0.533381i
$293$	−1651.91			−0.329372			−0.164686	−	0.986346i	$-0.552661\pi$
$293$	−1651.91			−0.329372			−0.164686	+	0.986346i	$0.552661\pi$
$294$		0			0
$295$	8411.50			1.66012
$296$	1161.48	+	2011.75i	0.228074	+	0.395035i
$297$		0			0
$298$	−2937.71	+	5088.26i	−0.571063	+	0.989110i
$299$	−4686.58	−	8117.39i	−0.906460	−	1.57004i
$300$		0			0
$301$		0			0
$302$	−3646.65			−0.694838
$303$		0			0
$304$	−642.709	+	1113.21i	−0.121256	+	0.210022i
$305$	−173.259	+	300.093i	−0.0325271	+	0.0563386i
$306$		0			0
$307$	−1016.42			−0.188958			−0.0944791	−	0.995527i	$-0.530119\pi$
$307$	−1016.42			−0.188958			−0.0944791	+	0.995527i	$0.530119\pi$
$308$		0			0
$309$		0			0
$310$	2543.59	+	4405.64i	0.466021	+	0.807172i
$311$	−4596.53	+	7961.42i	−0.838087	+	1.45161i	0.0534049	+	0.998573i	$0.482993\pi$
$311$	−4596.53	+	7961.42i	−0.838087	+	1.45161i	−0.891492	+	0.453037i	$0.850341\pi$
$312$		0			0
$313$	−3346.30	−	5795.97i	−0.604295	−	1.04667i	−0.992162	−	0.124954i	$-0.960122\pi$
$313$	−3346.30	−	5795.97i	−0.604295	−	1.04667i	0.387868	−	0.921715i	$-0.373212\pi$
$314$	1267.30			0.227763
$315$		0			0
$316$	−1674.92			−0.298169
$317$	−3526.25	−	6107.64i	−0.624775	−	1.08214i	−0.988584	−	0.150669i	$-0.951857\pi$
$317$	−3526.25	−	6107.64i	−0.624775	−	1.08214i	0.363809	−	0.931473i	$-0.381476\pi$
$318$		0			0
$319$	2601.53	−	4505.98i	0.456607	−	0.790866i
$320$	334.279	+	578.988i	0.0583962	+	0.101145i
$321$		0			0
$322$		0			0
$323$	1643.91			0.283187
$324$		0			0
$325$	470.190	−	814.393i	0.0802506	−	0.138998i
$326$	−1345.71	+	2330.83i	−0.228625	+	0.395990i
$327$		0			0
$328$	1344.00			0.226250
$329$		0			0
$330$		0			0
$331$	−1570.19	−	2719.64i	−0.260741	−	0.451616i	0.705698	−	0.708513i	$-0.250633\pi$
$331$	−1570.19	−	2719.64i	−0.260741	−	0.451616i	−0.966439	+	0.256896i	$0.917300\pi$
$332$	1523.43	−	2638.65i	0.251834	−	0.436190i
$333$		0			0
$334$	387.922	+	671.900i	0.0635513	+	0.110074i
$335$	2897.60			0.472575
$336$		0			0
$337$	2743.87			0.443526			0.221763	−	0.975101i	$-0.428819\pi$
$337$	2743.87			0.443526			0.221763	+	0.975101i	$0.428819\pi$
$338$	1311.32	+	2271.28i	0.211026	+	0.365507i
$339$		0			0
$340$	427.506	−	740.462i	0.0681905	−	0.118109i
$341$	−7441.62	−	12889.3i	−1.18178	−	2.04690i
$342$		0			0
$343$		0			0
$344$	−61.0347			−0.00956619
$345$		0			0
$346$	−622.660	+	1078.48i	−0.0967468	+	0.167570i
$347$	−5218.45	+	9038.62i	−0.807323	+	1.39832i	0.107389	+	0.994217i	$0.465751\pi$
$347$	−5218.45	+	9038.62i	−0.807323	+	1.39832i	−0.914712	+	0.404107i	$0.867582\pi$
$348$		0			0
$349$	2257.01			0.346175			0.173087	−	0.984906i	$-0.444626\pi$
$349$	2257.01			0.346175			0.173087	+	0.984906i	$0.444626\pi$
$350$		0			0
$351$		0			0
$352$	−977.977	−	1693.91i	−0.148086	−	0.256493i
$353$	2808.22	−	4863.98i	0.423418	−	0.733381i	−0.572854	−	0.819658i	$-0.694164\pi$
$353$	2808.22	−	4863.98i	0.423418	−	0.733381i	0.996271	+	0.0862770i	$0.0274970\pi$
$354$		0			0
$355$	3298.42	+	5713.04i	0.493133	+	0.854131i
$356$	−6288.38			−0.936190
$357$		0			0
$358$	−899.861			−0.132847
$359$	397.795	+	689.002i	0.0584815	+	0.101293i	0.893784	−	0.448498i	$-0.148041\pi$
$359$	397.795	+	689.002i	0.0584815	+	0.101293i	−0.835302	+	0.549791i	$0.814707\pi$
$360$		0			0
$361$	202.349	−	350.479i	0.0295013	−	0.0510977i
$362$	−184.353	−	319.309i	−0.0267662	−	0.0463605i
$363$		0			0
$364$		0			0
$365$	−8025.66			−1.15091
$366$		0			0
$367$	4096.99	−	7096.19i	0.582727	−	1.00931i	−0.412427	−	0.910990i	$-0.635319\pi$
$367$	4096.99	−	7096.19i	0.582727	−	1.00931i	0.995155	−	0.0983227i	$-0.0313477\pi$
$368$	−1265.98	+	2192.74i	−0.179330	+	0.310609i
$369$		0			0
$370$	6066.55			0.852392
$371$		0			0
$372$		0			0
$373$	−7038.69	−	12191.4i	−0.977076	−	1.69235i	−0.672906	−	0.739728i	$-0.734954\pi$
$373$	−7038.69	−	12191.4i	−0.977076	−	1.69235i	−0.304170	−	0.952618i	$-0.598379\pi$
$374$	−1250.72	+	2166.32i	−0.172923	+	0.299512i
$375$		0			0
$376$	−677.163	−	1172.88i	−0.0928777	−	0.160869i
$377$	5041.96			0.688791
$378$		0			0
$379$	6221.22			0.843173			0.421587	−	0.906788i	$-0.361473\pi$
$379$	6221.22			0.843173			0.421587	+	0.906788i	$0.361473\pi$
$380$	1678.47	+	2907.20i	0.226589	+	0.392463i
$381$		0			0
$382$	−350.965	+	607.890i	−0.0470077	+	0.0814197i
$383$	−5350.71	−	9267.70i	−0.713860	−	1.23644i	−0.963397	−	0.268077i	$-0.913612\pi$
$383$	−5350.71	−	9267.70i	−0.713860	−	1.23644i	0.249537	−	0.968365i	$-0.419722\pi$
$384$		0			0
$385$		0			0
$386$	−3056.52			−0.403038
$387$		0			0
$388$	2090.33	−	3620.56i	0.273506	−	0.473726i
$389$	−2110.81	+	3656.03i	−0.275121	+	0.476524i	−0.970166	−	0.242443i	$-0.922051\pi$
$389$	−2110.81	+	3656.03i	−0.275121	+	0.476524i	0.695044	+	0.718967i	$0.255385\pi$
$390$		0			0
$391$	3238.09			0.418816
$392$		0			0
$393$		0			0
$394$	−2874.65	−	4979.04i	−0.367570	−	0.636651i
$395$	−2187.07	+	3788.12i	−0.278591	+	0.482534i
$396$		0			0
$397$	−6037.87	−	10457.9i	−0.763305	−	1.32208i	−0.941138	−	0.338023i	$-0.890242\pi$
$397$	−6037.87	−	10457.9i	−0.763305	−	1.32208i	0.177833	−	0.984061i	$-0.443091\pi$
$398$	9897.41			1.24651
$399$		0			0
$400$	−254.023			−0.0317529
$401$	2753.19	+	4768.66i	0.342862	+	0.593855i	0.984963	−	0.172766i	$-0.0552703\pi$
$401$	2753.19	+	4768.66i	0.342862	+	0.593855i	−0.642101	+	0.766620i	$0.721937\pi$
$402$		0			0
$403$	7211.22	−	12490.2i	0.891356	−	1.54387i
$404$	−1951.84	−	3380.69i	−0.240366	−	0.416326i
$405$		0			0
$406$		0			0
$407$	−17748.5			−2.16157
$408$		0			0
$409$	714.089	−	1236.84i	0.0863311	−	0.149530i	−0.819627	−	0.572898i	$-0.805819\pi$
$409$	714.089	−	1236.84i	0.0863311	−	0.149530i	0.905958	+	0.423368i	$0.139152\pi$
$410$	1754.97	−	3039.69i	0.211394	−	0.366145i
$411$		0			0
$412$	2572.58			0.307626
$413$		0			0
$414$		0			0
$415$	−3978.52	−	6890.99i	−0.470597	−	0.815097i
$416$	947.698	−	1641.46i	0.111694	−	0.193460i
$417$		0			0
$418$	−4910.58	−	8505.38i	−0.574604	−	0.995244i
$419$	−264.960			−0.0308929			−0.0154465	−	0.999881i	$-0.504917\pi$
$419$	−264.960			−0.0308929			−0.0154465	+	0.999881i	$0.504917\pi$
$420$		0			0
$421$	−281.066			−0.0325375			−0.0162688	−	0.999868i	$-0.505179\pi$
$421$	−281.066			−0.0325375			−0.0162688	+	0.999868i	$0.505179\pi$
$422$	−5280.90	−	9146.78i	−0.609171	−	1.05511i
$423$		0			0
$424$	1000.45	−	1732.83i	0.114590	−	0.198475i
$425$	162.434	+	281.343i	0.0185393	+	0.0321110i
$426$		0			0
$427$		0			0
$428$	1246.38			0.140762
$429$		0			0
$430$	−79.6978	+	138.041i	−0.00893806	+	0.0154812i
$431$	893.189	−	1547.05i	0.0998223	−	0.172897i	−0.811789	−	0.583951i	$-0.801506\pi$
$431$	893.189	−	1547.05i	0.0998223	−	0.172897i	0.911611	+	0.411054i	$0.134839\pi$
$432$		0			0
$433$	−184.621			−0.0204904			−0.0102452	−	0.999948i	$-0.503261\pi$
$433$	−184.621			−0.0204904			−0.0102452	+	0.999948i	$0.503261\pi$
$434$		0			0
$435$		0			0
$436$	3731.66	+	6463.43i	0.409895	+	0.709959i
$437$	−6356.68	+	11010.1i	−0.695838	+	1.20523i
$438$		0			0
$439$	5637.32	+	9764.12i	0.612881	+	1.06154i	0.990752	+	0.135682i	$0.0433227\pi$
$439$	5637.32	+	9764.12i	0.612881	+	1.06154i	−0.377872	+	0.925858i	$0.623344\pi$
$440$	−5108.08			−0.553451
$441$		0			0
$442$	−2424.00			−0.260855
$443$	−3984.92	−	6902.09i	−0.427380	−	0.740244i	0.569259	−	0.822158i	$-0.307230\pi$
$443$	−3984.92	−	6902.09i	−0.427380	−	0.740244i	−0.996639	+	0.0819142i	$0.973897\pi$
$444$		0			0
$445$	−8211.23	+	14222.3i	−0.874718	+	1.51506i
$446$	−3996.57	−	6922.25i	−0.424311	−	0.734929i
$447$		0			0
$448$		0			0
$449$	8850.37			0.930233			0.465117	−	0.885249i	$-0.346012\pi$
$449$	8850.37			0.930233			0.465117	+	0.885249i	$0.346012\pi$
$450$		0			0
$451$	−5134.38	+	8893.00i	−0.536072	+	0.928504i
$452$	−3440.99	+	5959.97i	−0.358076	+	0.620206i
$453$		0			0
$454$	−1077.18			−0.111354
$455$		0			0
$456$		0			0
$457$	6513.65	+	11282.0i	0.666730	+	1.15481i	0.978813	+	0.204756i	$0.0656400\pi$
$457$	6513.65	+	11282.0i	0.666730	+	1.15481i	−0.312083	+	0.950055i	$0.601027\pi$
$458$	−4171.61	+	7225.44i	−0.425604	+	0.737167i
$459$		0			0
$460$	3306.17	+	5726.45i	0.335111	+	0.580429i
$461$	−1261.05			−0.127403			−0.0637016	−	0.997969i	$-0.520291\pi$
$461$	−1261.05			−0.127403			−0.0637016	+	0.997969i	$0.520291\pi$
$462$		0			0
$463$	−4005.47			−0.402052			−0.201026	−	0.979586i	$-0.564427\pi$
$463$	−4005.47			−0.402052			−0.201026	+	0.979586i	$0.564427\pi$
$464$	−680.988	−	1179.51i	−0.0681338	−	0.118011i
$465$		0			0
$466$	1539.73	−	2666.89i	0.153061	−	0.265110i
$467$	8548.91	+	14807.1i	0.847101	+	1.46722i	0.883784	+	0.467895i	$0.154988\pi$
$467$	8548.91	+	14807.1i	0.847101	+	1.46722i	−0.0366825	+	0.999327i	$0.511679\pi$
$468$		0			0
$469$		0			0
$470$	−3536.90			−0.347117
$471$		0			0
$472$	−3220.88	+	5578.72i	−0.314095	+	0.544029i
$473$	233.166	−	403.856i	0.0226659	−	0.0392586i
$474$		0			0
$475$	−1275.49			−0.123208
$476$		0			0
$477$		0			0
$478$	3132.67	+	5425.95i	0.299760	+	0.519199i
$479$	5844.26	−	10122.6i	0.557477	−	0.965578i	−0.440230	−	0.897885i	$-0.645103\pi$
$479$	5844.26	−	10122.6i	0.557477	−	0.965578i	0.997706	−	0.0676925i	$-0.0215637\pi$
$480$		0			0
$481$	−8599.49	−	14894.8i	−0.815183	−	1.41194i
$482$	5213.39			0.492662
$483$		0			0
$484$	9620.36			0.903489
$485$	−5459.01	−	9455.28i	−0.511095	−	0.885242i
$486$		0			0
$487$	4812.40	−	8335.31i	0.447783	−	0.775583i	−0.550458	−	0.834863i	$-0.685547\pi$
$487$	4812.40	−	8335.31i	0.447783	−	0.775583i	0.998241	+	0.0592793i	$0.0188803\pi$
$488$	−132.686	−	229.819i	−0.0123082	−	0.0213185i
$489$		0			0
$490$		0			0
$491$	−6320.63			−0.580949			−0.290475	−	0.956883i	$-0.593813\pi$
$491$	−6320.63			−0.580949			−0.290475	+	0.956883i	$0.593813\pi$
$492$		0			0
$493$	−870.908	+	1508.46i	−0.0795613	+	0.137804i
$494$	4758.55	−	8242.05i	0.433395	−	0.750662i
$495$		0			0
$496$	−3895.91			−0.352684
$497$		0			0
$498$		0			0
$499$	7527.29	+	13037.6i	0.675286	+	1.16963i	0.976385	+	0.216037i	$0.0693130\pi$
$499$	7527.29	+	13037.6i	0.675286	+	1.16963i	−0.301100	+	0.953593i	$0.597354\pi$
$500$	−2943.25	+	5097.86i	−0.263253	+	0.455967i
$501$		0			0
$502$	3426.24	+	5934.42i	0.304623	+	0.527622i
$503$	−16559.1			−1.46786			−0.733930	−	0.679225i	$-0.762316\pi$
$503$	−16559.1			−1.46786			−0.733930	+	0.679225i	$0.762316\pi$
$504$		0			0
$505$	−10194.7			−0.898333
$506$	−9672.63	−	16753.5i	−0.849804	−	1.47190i
$507$		0			0
$508$	−284.471	+	492.718i	−0.0248452	+	0.0430332i
$509$	−6669.48	−	11551.9i	−0.580785	−	1.00595i	−0.995387	−	0.0959462i	$-0.969412\pi$
$509$	−6669.48	−	11551.9i	−0.580785	−	1.00595i	0.414601	−	0.910003i	$-0.363921\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−5857.44	+	10145.4i	−0.502647	+	0.870610i
$515$	3359.21	−	5818.33i	0.287426	−	0.497837i
$516$		0			0
$517$	10347.6			0.880250
$518$		0			0
$519$		0			0
$520$	−2474.97	−	4286.77i	−0.208720	−	0.361514i
$521$	−3591.35	+	6220.40i	−0.301996	+	0.523072i	−0.976588	−	0.215118i	$-0.930986\pi$
$521$	−3591.35	+	6220.40i	−0.301996	+	0.523072i	0.674592	+	0.738191i	$0.264320\pi$
$522$		0			0
$523$	4815.07	+	8339.94i	0.402578	+	0.697285i	0.994036	−	0.109050i	$-0.0347810\pi$
$523$	4815.07	+	8339.94i	0.402578	+	0.697285i	−0.591459	+	0.806335i	$0.701448\pi$
$524$	−9946.04			−0.829189
$525$		0			0
$526$	2171.86			0.180034
$527$	2491.22	+	4314.91i	0.205919	+	0.356661i
$528$		0			0
$529$	−6437.57	+	11150.2i	−0.529101	+	0.916430i
$530$	−2612.73	−	4525.37i	−0.214131	−	0.370886i
$531$		0			0
$532$		0			0
$533$	−9950.83			−0.808664
$534$		0			0
$535$	1627.49	−	2818.90i	0.131519	−	0.227798i
$536$	−1109.53	+	1921.76i	−0.0894111	+	0.154865i
$537$		0			0
$538$	−11158.9			−0.894228
$539$		0			0
$540$		0			0
$541$	−7774.74	−	13466.2i	−0.617860	−	1.07016i	−0.989875	−	0.141938i	$-0.954667\pi$
$541$	−7774.74	−	13466.2i	−0.617860	−	1.07016i	0.372016	−	0.928227i	$-0.378667\pi$
$542$	560.327	−	970.515i	0.0444061	−	0.0769136i
$543$		0			0
$544$	327.396	+	567.066i	0.0258032	+	0.0446925i
$545$	19490.9			1.53192
$546$		0			0
$547$	−5917.38			−0.462539			−0.231270	−	0.972890i	$-0.574288\pi$
$547$	−5917.38			−0.462539			−0.231270	+	0.972890i	$0.574288\pi$
$548$	5194.42	+	8997.01i	0.404918	+	0.701338i
$549$		0			0
$550$	970.425	−	1680.83i	0.0752346	−	0.130310i
$551$	−3419.36	−	5922.50i	−0.264373	−	0.457907i
$552$		0			0
$553$		0			0
$554$	9016.15			0.691444
$555$		0			0
$556$	3201.04	−	5544.37i	0.244163	−	0.422902i
$557$	−1065.93	+	1846.25i	−0.0810862	+	0.140445i	−0.903717	−	0.428131i	$-0.859172\pi$
$557$	−1065.93	+	1846.25i	−0.0810862	+	0.140445i	0.822631	+	0.568576i	$0.192506\pi$
$558$		0			0
$559$	451.894			0.0341916
$560$		0			0
$561$		0			0
$562$	−4329.75	−	7499.35i	−0.324981	−	0.562884i
$563$	−3687.95	+	6387.72i	−0.276072	+	0.478171i	−0.970405	−	0.241483i	$-0.922366\pi$
$563$	−3687.95	+	6387.72i	−0.276072	+	0.478171i	0.694333	+	0.719654i	$0.255700\pi$
$564$		0			0
$565$	8986.33	+	15564.8i	0.669129	+	1.15897i
$566$	−1742.10			−0.129375
$567$		0			0
$568$	−5052.05			−0.373203
$569$	6350.42	+	10999.3i	0.467880	+	0.810391i	0.999326	−	0.0367005i	$-0.0116847\pi$
$569$	6350.42	+	10999.3i	0.467880	+	0.810391i	−0.531447	+	0.847092i	$0.678351\pi$
$570$		0			0
$571$	3845.06	−	6659.84i	0.281805	−	0.488101i	−0.690024	−	0.723786i	$-0.742400\pi$
$571$	3845.06	−	6659.84i	0.281805	−	0.488101i	0.971829	+	0.235686i	$0.0757335\pi$
$572$	7240.83	+	12541.5i	0.529291	+	0.916759i
$573$		0			0
$574$		0			0
$575$	−2512.40			−0.182216
$576$		0			0
$577$	1547.43	−	2680.23i	0.111647	−	0.193379i	−0.804787	−	0.593563i	$-0.797721\pi$
$577$	1547.43	−	2680.23i	0.111647	−	0.193379i	0.916435	+	0.400185i	$0.131054\pi$
$578$	−4494.30	+	7784.35i	−0.323422	+	0.560184i
$579$		0			0
$580$	−3556.88			−0.254640
$581$		0			0
$582$		0			0
$583$	7643.87	+	13239.6i	0.543013	+	0.940526i
$584$	3073.13	−	5322.82i	0.217752	−	0.377158i
$585$		0			0
$586$	−1651.91	−	2861.20i	−0.116450	−	0.201698i
$587$	9967.83			0.700880			0.350440	−	0.936585i	$-0.386032\pi$
$587$	9967.83			0.700880			0.350440	+	0.936585i	$0.386032\pi$
$588$		0			0
$589$	−19562.0			−1.36849
$590$	8411.50	+	14569.1i	0.586942	+	1.01661i
$591$		0			0
$592$	−2322.97	+	4023.49i	−0.161272	+	0.279332i
$593$	884.864	+	1532.63i	0.0612766	+	0.106134i	0.895036	−	0.445993i	$-0.147149\pi$
$593$	884.864	+	1532.63i	0.0612766	+	0.106134i	−0.833760	+	0.552127i	$0.813816\pi$
$594$		0			0
$595$		0			0
$596$	−11750.8			−0.807605
$597$		0			0
$598$	9373.15	−	16234.8i	0.640964	−	1.11018i
$599$	3173.66	−	5496.95i	0.216481	−	0.374957i	−0.737248	−	0.675622i	$-0.763875\pi$
$599$	3173.66	−	5496.95i	0.216481	−	0.374957i	0.953730	+	0.300665i	$0.0972086\pi$
$600$		0			0
$601$	−22005.7			−1.49356			−0.746781	−	0.665070i	$-0.768401\pi$
$601$	−22005.7			−1.49356			−0.746781	+	0.665070i	$0.768401\pi$
$602$		0			0
$603$		0			0
$604$	−3646.65	−	6316.18i	−0.245662	−	0.425500i
$605$	12562.0	−	21758.1i	0.844165	−	1.46214i
$606$		0			0
$607$	8853.55	+	15334.8i	0.592017	+	1.02540i	0.993960	+	0.109740i	$0.0350017\pi$
$607$	8853.55	+	15334.8i	0.592017	+	1.02540i	−0.401943	+	0.915665i	$0.631665\pi$
$608$	−2570.84			−0.171482
$609$		0			0
$610$	−693.035			−0.0460003
$611$	5013.64	+	8683.87i	0.331964	+	0.574979i
$612$		0			0
$613$	−7923.32	+	13723.6i	−0.522055	+	0.904226i	0.477616	+	0.878569i	$0.341501\pi$
$613$	−7923.32	+	13723.6i	−0.522055	+	0.904226i	−0.999671	+	0.0256570i	$0.991832\pi$
$614$	−1016.42	−	1760.49i	−0.0668068	−	0.115713i
$615$		0			0
$616$		0			0
$617$	29473.4			1.92311			0.961553	−	0.274621i	$-0.0885524\pi$
$617$	29473.4			1.92311			0.961553	+	0.274621i	$0.0885524\pi$
$618$		0			0
$619$	5763.74	−	9983.08i	0.374255	−	0.648229i	−0.615960	−	0.787778i	$-0.711232\pi$
$619$	5763.74	−	9983.08i	0.374255	−	0.648229i	0.990215	+	0.139548i	$0.0445650\pi$
$620$	−5087.19	+	8811.27i	−0.329527	+	0.570757i
$621$		0			0
$622$	−18386.1			−1.18523
$623$		0			0
$624$		0			0
$625$	6694.19	+	11594.7i	0.428428	+	0.742059i
$626$	6692.61	−	11591.9i	0.427301	−	0.740107i
$627$		0			0
$628$	1267.30	+	2195.02i	0.0805265	+	0.139476i
$629$	5941.63			0.376643
$630$		0			0
$631$	25846.1			1.63062			0.815308	−	0.579027i	$-0.196568\pi$
$631$	25846.1			1.63062			0.815308	+	0.579027i	$0.196568\pi$
$632$	−1674.92	−	2901.04i	−0.105419	−	0.182591i
$633$		0			0
$634$	7052.49	−	12215.3i	0.441783	−	0.765190i
$635$	742.912	+	1286.76i	0.0464277	+	0.0804151i
$636$		0			0
$637$		0			0
$638$	10406.1			0.645739
$639$		0			0
$640$	−668.558	+	1157.98i	−0.0412923	+	0.0715204i
$641$	−2767.39	+	4793.26i	−0.170523	+	0.295355i	−0.938603	−	0.344999i	$-0.887879\pi$
$641$	−2767.39	+	4793.26i	−0.170523	+	0.295355i	0.768080	+	0.640354i	$0.221212\pi$
$642$		0			0
$643$	−1634.56			−0.100250			−0.0501251	−	0.998743i	$-0.515962\pi$
$643$	−1634.56			−0.100250			−0.0501251	+	0.998743i	$0.515962\pi$
$644$		0			0
$645$		0			0
$646$	1643.91	+	2847.33i	0.100122	+	0.173416i
$647$	3769.00	−	6528.10i	0.229018	−	0.396671i	−0.728499	−	0.685047i	$-0.759782\pi$
$647$	3769.00	−	6528.10i	0.229018	−	0.396671i	0.957517	+	0.288375i	$0.0931151\pi$
$648$		0			0
$649$	−24608.9	−	42623.9i	−1.48842	−	2.57802i
$650$	1880.76			0.113491
$651$		0			0
$652$	−5382.83			−0.323325
$653$	6656.09	+	11528.7i	0.398887	+	0.690892i	0.993589	−	0.113054i	$-0.0360634\pi$
$653$	6656.09	+	11528.7i	0.398887	+	0.690892i	−0.594702	+	0.803946i	$0.702730\pi$
$654$		0			0
$655$	−12987.3	+	22494.7i	−0.774743	+	1.34189i
$656$	1344.00	+	2327.88i	0.0799914	+	0.138549i
$657$		0			0
$658$		0			0
$659$	10962.0			0.647981			0.323991	−	0.946060i	$-0.394975\pi$
$659$	10962.0			0.647981			0.323991	+	0.946060i	$0.394975\pi$
$660$		0			0
$661$	−11816.3	+	20466.4i	−0.695309	+	1.20431i	0.274767	+	0.961511i	$0.411399\pi$
$661$	−11816.3	+	20466.4i	−0.695309	+	1.20431i	−0.970076	+	0.242800i	$0.921934\pi$
$662$	3140.37	−	5439.28i	0.184372	−	0.319341i
$663$		0			0
$664$	6093.71			0.356147
$665$		0			0
$666$		0			0
$667$	−6735.28	−	11665.8i	−0.390991	−	0.677216i
$668$	−775.843	+	1343.80i	−0.0449376	+	0.0778341i
$669$		0			0
$670$	2897.60	+	5018.78i	0.167080	+	0.289392i
$671$	2027.56			0.116652
$672$		0			0
$673$	23483.0			1.34503			0.672513	−	0.740085i	$-0.265215\pi$
$673$	23483.0			1.34503			0.672513	+	0.740085i	$0.265215\pi$
$674$	2743.87	+	4752.53i	0.156810	+	0.271603i
$675$		0			0
$676$	−2622.65	+	4542.56i	−0.149218	+	0.258452i
$677$	12336.2	+	21367.0i	0.700325	+	1.21300i	0.968352	+	0.249587i	$0.0802948\pi$
$677$	12336.2	+	21367.0i	0.700325	+	1.21300i	−0.268028	+	0.963411i	$0.586372\pi$
$678$		0			0
$679$		0			0
$680$	1710.02			0.0964359
$681$		0			0
$682$	14883.2	−	25778.5i	0.835643	−	1.44738i
$683$	−4469.73	+	7741.80i	−0.250409	+	0.433721i	−0.963638	−	0.267209i	$-0.913898\pi$
$683$	−4469.73	+	7741.80i	−0.250409	+	0.433721i	0.713229	+	0.700931i	$0.247232\pi$
$684$		0			0
$685$	27131.1			1.51332
$686$		0			0
$687$		0			0
$688$	−61.0347	−	105.715i	−0.00338216	−	0.00585807i
$689$	−7407.21	+	12829.7i	−0.409568	+	0.709392i
$690$		0			0
$691$	7555.03	+	13085.7i	0.415929	+	0.720410i	0.995525	−	0.0944937i	$-0.0301232\pi$
$691$	7555.03	+	13085.7i	0.415929	+	0.720410i	−0.579597	+	0.814904i	$0.696790\pi$
$692$	−2490.64			−0.136821
$693$		0			0
$694$	−20873.8			−1.14173
$695$	−8359.70	−	14479.4i	−0.456261	−	0.790268i
$696$		0			0
$697$	1718.83	−	2977.09i	0.0934077	−	0.161787i
$698$	2257.01	+	3909.26i	0.122391	+	0.211988i
$699$		0			0
$700$		0			0
$701$	18353.3			0.988865			0.494432	−	0.869216i	$-0.335376\pi$
$701$	18353.3			0.988865			0.494432	+	0.869216i	$0.335376\pi$
$702$		0			0
$703$	−11664.0	+	20202.6i	−0.625769	+	1.08386i
$704$	1955.95	−	3387.81i	0.104713	−	0.181368i
$705$		0			0
$706$	11232.9			0.598803
$707$		0			0
$708$		0			0
$709$	5036.85	+	8724.07i	0.266802	+	0.462115i	0.968034	−	0.250818i	$-0.0806997\pi$
$709$	5036.85	+	8724.07i	0.266802	+	0.462115i	−0.701232	+	0.712933i	$0.747366\pi$
$710$	−6596.85	+	11426.1i	−0.348698	+	0.603962i
$711$		0			0
$712$	−6288.38	−	10891.8i	−0.330993	−	0.573297i
$713$	−38532.3			−2.02391
$714$		0			0
$715$	37819.7			1.97815
$716$	−899.861	−	1558.61i	−0.0469684	−	0.0813517i
$717$		0			0
$718$	−795.591	+	1378.00i	−0.0413526	+	0.0716249i
$719$	9944.63	+	17224.6i	0.515817	+	0.893420i	0.999831	+	0.0183607i	$0.00584472\pi$
$719$	9944.63	+	17224.6i	0.515817	+	0.893420i	−0.484015	+	0.875060i	$0.660822\pi$
$720$		0			0
$721$		0			0
$722$	809.397			0.0417211
$723$		0			0
$724$	368.706	−	638.617i	0.0189266	−	0.0327818i
$725$	675.730	−	1170.40i	0.0346151	−	0.0599552i
$726$		0			0
$727$	−13403.5			−0.683780			−0.341890	−	0.939740i	$-0.611067\pi$
$727$	−13403.5			−0.683780			−0.341890	+	0.939740i	$0.611067\pi$
$728$		0			0
$729$		0			0
$730$	−8025.66	−	13900.9i	−0.406908	−	0.704786i
$731$	−78.0566	+	135.198i	−0.00394942	+	0.00684060i
$732$		0			0
$733$	6627.50	+	11479.2i	0.333960	+	0.578435i	0.983284	−	0.182076i	$-0.0582817\pi$
$733$	6627.50	+	11479.2i	0.333960	+	0.578435i	−0.649325	+	0.760511i	$0.724948\pi$
$734$	16387.9			0.824101
$735$		0			0
$736$	−5063.91			−0.253612
$737$	−8477.29	−	14683.1i	−0.423698	−	0.733866i
$738$		0			0
$739$	−7710.19	+	13354.4i	−0.383794	+	0.664751i	−0.991601	−	0.129334i	$-0.958716\pi$
$739$	−7710.19	+	13354.4i	−0.383794	+	0.664751i	0.607807	+	0.794085i	$0.292049\pi$
$740$	6066.55	+	10507.6i	0.301366	+	0.521981i
$741$		0			0
$742$		0			0
$743$	943.019			0.0465626			0.0232813	−	0.999729i	$-0.492589\pi$
$743$	943.019			0.0465626			0.0232813	+	0.999729i	$0.492589\pi$
$744$		0			0
$745$	−15344.0	+	26576.5i	−0.754576	+	1.30696i
$746$	14077.4	−	24382.7i	0.690897	−	1.19667i
$747$		0			0
$748$	−5002.89			−0.244551
$749$		0			0
$750$		0			0
$751$	14297.9	+	24764.7i	0.694726	+	1.20330i	0.970273	+	0.242013i	$0.0778076\pi$
$751$	14297.9	+	24764.7i	0.694726	+	1.20330i	−0.275547	+	0.961287i	$0.588859\pi$
$752$	1354.33	−	2345.76i	0.0656744	−	0.113751i
$753$		0			0
$754$	5041.96	+	8732.94i	0.243524	+	0.421797i
$755$	−19046.9			−0.918127
$756$		0			0
$757$	−28984.4			−1.39162			−0.695810	−	0.718226i	$-0.744955\pi$
$757$	−28984.4			−1.39162			−0.695810	+	0.718226i	$0.744955\pi$
$758$	6221.22	+	10775.5i	0.298107	+	0.516336i
$759$		0			0
$760$	−3356.94	+	5814.39i	−0.160222	+	0.277513i
$761$	4465.05	+	7733.70i	0.212691	+	0.368392i	0.952556	−	0.304364i	$-0.0984438\pi$
$761$	4465.05	+	7733.70i	0.212691	+	0.368392i	−0.739865	+	0.672756i	$0.765110\pi$
$762$		0			0
$763$		0			0
$764$	−1403.86			−0.0664789
$765$		0			0
$766$	10701.4	−	18535.4i	0.504776	−	0.874297i
$767$	23847.0	−	41304.3i	1.12264	−	1.94447i
$768$		0			0
$769$	−2373.15			−0.111285			−0.0556424	−	0.998451i	$-0.517721\pi$
$769$	−2373.15			−0.111285			−0.0556424	+	0.998451i	$0.517721\pi$
$770$		0			0
$771$		0			0
$772$	−3056.52	−	5294.04i	−0.142495	−	0.246809i
$773$	13988.5	−	24228.8i	0.650881	−	1.12736i	−0.332029	−	0.943269i	$-0.607733\pi$
$773$	13988.5	−	24228.8i	0.650881	−	1.12736i	0.982909	−	0.184089i	$-0.0589336\pi$
$774$		0			0
$775$	−1932.91	−	3347.90i	−0.0895900	−	0.155174i
$776$	8361.32			0.386796
$777$		0			0
$778$	−8443.23			−0.389080
$779$	6748.45	+	11688.7i	0.310383	+	0.537599i
$780$		0			0
$781$	19299.9	−	33428.5i	0.884259	−	1.53158i
$782$	3238.09	+	5608.53i	0.148074	+	0.256471i
$783$		0			0
$784$		0			0
$785$	6619.23			0.300956
$786$		0			0
$787$	17180.5	−	29757.4i	0.778167	−	1.34782i	−0.154831	−	0.987941i	$-0.549483\pi$
$787$	17180.5	−	29757.4i	0.778167	−	1.34782i	0.932997	−	0.359883i	$-0.117183\pi$
$788$	5749.30	−	9958.08i	0.259911	−	0.450180i
$789$		0			0
$790$	−8748.29			−0.393987
$791$		0			0
$792$		0			0
$793$	982.394	+	1701.56i	0.0439922	+	0.0761968i
$794$	12075.7	−	20915.8i	0.539738	−	0.934854i
$795$		0			0
$796$	9897.41	+	17142.8i	0.440709	+	0.763330i
$797$	10399.5			0.462196			0.231098	−	0.972930i	$-0.425768\pi$
$797$	10399.5			0.462196			0.231098	+	0.972930i	$0.425768\pi$
$798$		0			0
$799$	−3464.06			−0.153379
$800$	−254.023	−	439.981i	−0.0112263	−	0.0194446i
$801$		0			0
$802$	−5506.38	+	9537.33i	−0.242440	+	0.419919i
$803$	23480.1	+	40668.7i	1.03187	+	1.78726i
$804$		0			0
$805$		0			0
$806$	28844.9			1.26057
$807$		0			0
$808$	3903.69	−	6761.38i	0.169964	−	0.294387i
$809$	8971.53	−	15539.1i	0.389891	−	0.675312i	−0.602543	−	0.798086i	$-0.705846\pi$
$809$	8971.53	−	15539.1i	0.389891	−	0.675312i	0.992435	+	0.122775i	$0.0391792\pi$
$810$		0			0
$811$	571.663			0.0247519			0.0123760	−	0.999923i	$-0.496061\pi$
$811$	571.663			0.0247519			0.0123760	+	0.999923i	$0.496061\pi$
$812$		0			0
$813$		0			0
$814$	−17748.5	−	30741.3i	−0.764231	−	1.32369i
$815$	−7028.78	+	12174.2i	−0.302095	+	0.523244i
$816$		0			0
$817$	−306.465	−	530.814i	−0.0131235	−	0.0227305i
$818$	2856.36			0.122091
$819$		0			0
$820$	7019.86			0.298956
$821$	−6947.84	−	12034.0i	−0.295349	−	0.511559i	0.679717	−	0.733474i	$-0.262103\pi$
$821$	−6947.84	−	12034.0i	−0.295349	−	0.511559i	−0.975066	+	0.221915i	$0.928769\pi$
$822$		0			0
$823$	10814.6	−	18731.5i	0.458049	−	0.793364i	−0.540809	−	0.841145i	$-0.681882\pi$
$823$	10814.6	−	18731.5i	0.458049	−	0.793364i	0.998858	+	0.0477816i	$0.0152152\pi$
$824$	2572.58	+	4455.83i	0.108762	+	0.188381i
$825$		0			0
$826$		0			0
$827$	4700.10			0.197628			0.0988140	−	0.995106i	$-0.468495\pi$
$827$	4700.10			0.197628			0.0988140	+	0.995106i	$0.468495\pi$
$828$		0			0
$829$	−19055.4	+	33004.9i	−0.798337	+	1.38276i	0.122361	+	0.992486i	$0.460953\pi$
$829$	−19055.4	+	33004.9i	−0.798337	+	1.38276i	−0.920698	+	0.390275i	$0.872380\pi$
$830$	7957.03	−	13782.0i	0.332762	−	0.576361i
$831$		0			0
$832$	3790.79			0.157959
$833$		0			0
$834$		0			0
$835$	2026.16	+	3509.41i	0.0839738	+	0.145447i
$836$	9821.17	−	17010.8i	0.406307	−	0.703744i
$837$		0			0
$838$	−264.960	−	458.924i	−0.0109223	−	0.0189180i
$839$	−20080.2			−0.826277			−0.413138	−	0.910668i	$-0.635567\pi$
$839$	−20080.2			−0.826277			−0.413138	+	0.910668i	$0.635567\pi$
$840$		0			0
$841$	−17143.0			−0.702898
$842$	−281.066	−	486.820i	−0.0115038	−	0.0199251i
$843$		0			0
$844$	10561.8	−	18293.6i	0.430749	−	0.746079i
$845$	6849.19	+	11863.1i	0.278840	+	0.482964i
$846$		0			0
$847$		0			0
$848$	4001.79			0.162054
$849$		0			0
$850$	−324.867	+	562.687i	−0.0131092	+	0.0227059i
$851$	−22975.2	+	39794.1i	−0.925474	+	1.60297i
$852$		0			0
$853$	34906.8			1.40116			0.700578	−	0.713576i	$-0.252926\pi$
$853$	34906.8			1.40116			0.700578	+	0.713576i	$0.252926\pi$
$854$		0			0
$855$		0			0
$856$	1246.38	+	2158.79i	0.0497668	+	0.0861985i
$857$	24023.4	−	41609.7i	0.957553	−	1.65853i	0.229139	−	0.973394i	$-0.426409\pi$
$857$	24023.4	−	41609.7i	0.957553	−	1.65853i	0.728414	−	0.685137i	$-0.240258\pi$
$858$		0			0
$859$	−17603.1	−	30489.5i	−0.699198	−	1.21105i	−0.968745	−	0.248059i	$-0.920207\pi$
$859$	−17603.1	−	30489.5i	−0.699198	−	1.21105i	0.269547	−	0.962987i	$-0.413126\pi$
$860$	−318.791			−0.0126403
$861$		0			0
$862$	3572.76			0.141170
$863$	17928.8	+	31053.7i	0.707190	+	1.22489i	0.965895	+	0.258933i	$0.0833708\pi$
$863$	17928.8	+	31053.7i	0.707190	+	1.22489i	−0.258705	+	0.965956i	$0.583296\pi$
$864$		0			0
$865$	−3252.22	+	5633.01i	−0.127837	+	0.221420i
$866$	−184.621	−	319.773i	−0.00724444	−	0.0125477i
$867$		0			0
$868$		0			0
$869$	25594.3			0.999109
$870$		0			0
$871$	8214.83	−	14228.5i	0.319574	−	0.553518i
$872$	−7463.32	+	12926.9i	−0.289839	+	0.502017i
$873$		0			0
$874$	−25426.7			−0.984064
$875$		0			0
$876$		0			0
$877$	−3683.09	−	6379.30i	−0.141812	−	0.245625i	0.786367	−	0.617760i	$-0.211959\pi$
$877$	−3683.09	−	6379.30i	−0.141812	−	0.245625i	−0.928179	+	0.372134i	$0.878626\pi$
$878$	−11274.6	+	19528.2i	−0.433372	+	0.750622i
$879$		0			0
$880$	−5108.08	−	8847.46i	−0.195674	−	0.338918i
$881$	−3628.00			−0.138741			−0.0693703	−	0.997591i	$-0.522099\pi$
$881$	−3628.00			−0.138741			−0.0693703	+	0.997591i	$0.522099\pi$
$882$		0			0
$883$	25123.0			0.957483			0.478741	−	0.877956i	$-0.341093\pi$
$883$	25123.0			0.957483			0.478741	+	0.877956i	$0.341093\pi$
$884$	−2424.00	−	4198.49i	−0.0922262	−	0.159740i
$885$		0			0
$886$	7969.84	−	13804.2i	0.302203	−	0.523431i
$887$	−7887.38	−	13661.3i	−0.298571	−	0.517140i	0.677238	−	0.735764i	$-0.263177\pi$
$887$	−7887.38	−	13661.3i	−0.298571	−	0.517140i	−0.975809	+	0.218624i	$0.929843\pi$
$888$		0			0
$889$		0			0
$890$	−32844.9			−1.23704
$891$		0			0
$892$	7993.13	−	13844.5i	0.300033	−	0.519673i
$893$	6800.29	−	11778.5i	0.254830	−	0.441378i
$894$		0			0
$895$	−4700.07			−0.175538
$896$		0			0
$897$		0			0
$898$	8850.37	+	15329.3i	0.328887	+	0.569649i
$899$	10363.5	−	17950.2i	0.384476	−	0.665931i
$900$		0			0
$901$	−2558.92	−	4432.19i	−0.0946172	−	0.163882i
$902$	−20537.5			−0.758120
$903$		0			0
$904$	−13764.0			−0.506396
$905$	−962.896	−	1667.78i	−0.0353677	−	0.0612586i
$906$		0			0
$907$	2556.99	−	4428.84i	0.0936092	−	0.162136i	−0.815418	−	0.578872i	$-0.803493\pi$
$907$	2556.99	−	4428.84i	0.0936092	−	0.162136i	0.909027	+	0.416737i	$0.136826\pi$
$908$	−1077.18	−	1865.74i	−0.0393696	−	0.0681902i
$909$		0			0
$910$		0			0
$911$	10279.1			0.373834			0.186917	−	0.982376i	$-0.440150\pi$
$911$	10279.1			0.373834			0.186917	+	0.982376i	$0.440150\pi$
$912$		0			0
$913$	−23279.3	+	40321.0i	−0.843848	+	1.46159i
$914$	−13027.3	+	22563.9i	−0.471449	+	0.816574i
$915$		0			0
$916$	−16686.4			−0.601895
$917$		0			0
$918$		0			0
$919$	19461.0	+	33707.4i	0.698540	+	1.20991i	0.968973	+	0.247168i	$0.0794999\pi$
$919$	19461.0	+	33707.4i	0.698540	+	1.20991i	−0.270433	+	0.962739i	$0.587167\pi$
$920$	−6612.34	+	11452.9i	−0.236959	+	0.410425i
$921$		0			0
$922$	−1261.05	−	2184.20i	−0.0450439	−	0.0780182i
$923$	37404.8			1.33390
$924$		0			0
$925$	−4610.05			−0.163868
$926$	−4005.47	−	6937.67i	−0.142147	−	0.246205i
$927$		0			0
$928$	1361.98	−	2359.01i	0.0481779	−	0.0834466i
$929$	−7483.82	−	12962.4i	−0.264302	−	0.457784i	0.703079	−	0.711112i	$-0.251808\pi$
$929$	−7483.82	−	12962.4i	−0.264302	−	0.457784i	−0.967380	+	0.253328i	$0.918475\pi$
$930$		0			0
$931$		0			0
$932$	6158.92			0.216461
$933$		0			0
$934$	−17097.8	+	29614.3i	−0.598991	+	1.03748i
$935$	−6532.67	+	11314.9i	−0.228493	+	0.395762i
$936$		0			0
$937$	22353.0			0.779339			0.389669	−	0.920955i	$-0.372589\pi$
$937$	22353.0			0.779339			0.389669	+	0.920955i	$0.372589\pi$
$938$		0			0
$939$		0			0
$940$	−3536.90	−	6126.08i	−0.122724	−	0.212565i
$941$	−6690.77	+	11588.7i	−0.231788	+	0.401469i	−0.958334	−	0.285649i	$-0.907791\pi$
$941$	−6690.77	+	11588.7i	−0.231788	+	0.401469i	0.726546	+	0.687118i	$0.241124\pi$
$942$		0			0
$943$	13292.8	+	23023.7i	0.459037	+	0.795075i
$944$	−12883.5			−0.444198
$945$		0			0
$946$	932.665			0.0320545
$947$	316.888	+	548.867i	0.0108738	+	0.0188340i	0.871411	−	0.490553i	$-0.163205\pi$
$947$	316.888	+	548.867i	0.0108738	+	0.0188340i	−0.860537	+	0.509387i	$0.829872\pi$
$948$		0			0
$949$	−22753.1	+	39409.6i	−0.778291	+	1.34804i
$950$	−1275.49	−	2209.22i	−0.0435605	−	0.0754489i
$951$		0			0
$952$		0			0
$953$	−49340.0			−1.67710			−0.838551	−	0.544823i	$-0.816597\pi$
$953$	−49340.0			−1.67710			−0.838551	+	0.544823i	$0.816597\pi$
$954$		0			0
$955$	−1833.13	+	3175.08i	−0.0621138	+	0.107584i
$956$	−6265.34	+	10851.9i	−0.211962	+	0.367129i
$957$		0			0
$958$	23377.1			0.788391
$959$		0			0
$960$		0			0
$961$	−14749.2	−	25546.4i	−0.495090	−	0.857520i
$962$	17199.0	−	29789.5i	0.576421	−	0.998391i
$963$		0			0
$964$	5213.39	+	9029.85i	0.174182	+	0.301693i
$965$	−15964.5			−0.532556
$966$		0			0
$967$	−3340.71			−0.111096			−0.0555480	−	0.998456i	$-0.517691\pi$
$967$	−3340.71			−0.111096			−0.0555480	+	0.998456i	$0.517691\pi$
$968$	9620.36	+	16662.9i	0.319432	+	0.553272i
$969$		0			0
$970$	10918.0	−	18910.6i	0.361398	−	0.625960i
$971$	−2435.20	−	4217.89i	−0.0804833	−	0.139401i	0.822974	−	0.568079i	$-0.192313\pi$
$971$	−2435.20	−	4217.89i	−0.0804833	−	0.139401i	−0.903458	+	0.428677i	$0.858980\pi$
$972$		0			0
$973$		0			0
$974$	19249.6			0.633261
$975$		0			0
$976$	265.372	−	459.638i	0.00870324	−	0.0150745i
$977$	3420.67	−	5924.78i	0.112013	−	0.194013i	−0.804569	−	0.593860i	$-0.797603\pi$
$977$	3420.67	−	5924.78i	0.112013	−	0.194013i	0.916582	+	0.399847i	$0.130937\pi$
$978$		0			0
$979$	96092.1			3.13699
$980$		0			0
$981$		0			0
$982$	−6320.63	−	10947.7i	−0.205397	−	0.355757i
$983$	5344.94	−	9257.71i	0.173425	−	0.300382i	−0.766190	−	0.642614i	$-0.777850\pi$
$983$	5344.94	−	9257.71i	0.173425	−	0.300382i	0.939615	+	0.342233i	$0.111183\pi$
$984$		0			0
$985$	−15014.6	−	26006.1i	−0.485691	−	0.841241i
$986$	−3483.63			−0.112517
$987$		0			0
$988$	19034.2			0.612913
$989$	−603.660	−	1045.57i	−0.0194088	−	0.0336170i
$990$		0			0
$991$	−3732.84	+	6465.48i	−0.119655	+	0.207248i	−0.919631	−	0.392784i	$-0.871512\pi$
$991$	−3732.84	+	6465.48i	−0.119655	+	0.207248i	0.799976	+	0.600032i	$0.204845\pi$
$992$	−3895.91	−	6747.91i	−0.124693	−	0.215974i
$993$		0			0
$994$		0			0
$995$	51695.3			1.64709
$996$		0			0
$997$	−8677.41	+	15029.7i	−0.275643	+	0.477428i	−0.970297	−	0.241916i	$-0.922224\pi$
$997$	−8677.41	+	15029.7i	−0.275643	+	0.477428i	0.694654	+	0.719344i	$0.255557\pi$
$998$	−15054.6	+	26075.3i	−0.477499	+	0.827053i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.bj.361.2		4
3.2	odd	2		882.4.g.z.361.1		4
7.2	even	3	inner	882.4.g.bj.667.2		4
7.3	odd	6		882.4.a.ba.1.2		2
7.4	even	3		882.4.a.u.1.1		2
7.5	odd	6		126.4.g.f.37.1	yes	4
7.6	odd	2		126.4.g.f.109.1	yes	4
21.2	odd	6		882.4.g.z.667.1		4
21.5	even	6		126.4.g.e.37.2	✓	4
21.11	odd	6		882.4.a.bh.1.2		2
21.17	even	6		882.4.a.bd.1.1		2
21.20	even	2		126.4.g.e.109.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.g.e.37.2	✓	4	21.5	even	6
126.4.g.e.109.2	yes	4	21.20	even	2
126.4.g.f.37.1	yes	4	7.5	odd	6
126.4.g.f.109.1	yes	4	7.6	odd	2
882.4.a.u.1.1		2	7.4	even	3
882.4.a.ba.1.2		2	7.3	odd	6
882.4.a.bd.1.1		2	21.17	even	6
882.4.a.bh.1.2		2	21.11	odd	6
882.4.g.z.361.1		4	3.2	odd	2
882.4.g.z.667.1		4	21.2	odd	6
882.4.g.bj.361.2		4	1.1	even	1	trivial
882.4.g.bj.667.2		4	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.22311 + 9.04669i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.22311 + 9.04669i) q^{5} -8.00000 q^{8} +(-10.4462 + 18.0934i) q^{10} +(30.5618 - 52.9346i) q^{11} +59.2311 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-10.2311 + 17.7208i) q^{17} +(-40.1693 - 69.5753i) q^{19} -41.7849 q^{20} +122.247 q^{22} +(-79.1236 - 137.046i) q^{23} +(7.93822 - 13.7494i) q^{25} +(59.2311 + 102.591i) q^{26} +85.1236 q^{29} +(121.747 - 210.872i) q^{31} +(16.0000 - 27.7128i) q^{32} -40.9244 q^{34} +(-145.185 - 251.468i) q^{37} +(80.3387 - 139.151i) q^{38} +(-41.7849 - 72.3735i) q^{40} -168.000 q^{41} +7.62934 q^{43} +(122.247 + 211.738i) q^{44} +(158.247 - 274.092i) q^{46} +(84.6453 + 146.610i) q^{47} +31.7529 q^{50} +(-118.462 + 205.183i) q^{52} +(-125.056 + 216.603i) q^{53} +638.510 q^{55} +(85.1236 + 147.438i) q^{58} +(402.610 - 697.341i) q^{59} +(16.5858 + 28.7274i) q^{61} +486.988 q^{62} +64.0000 q^{64} +(309.371 + 535.846i) q^{65} +(138.691 - 240.220i) q^{67} +(-40.9244 - 70.8832i) q^{68} +631.506 q^{71} +(-384.142 + 665.353i) q^{73} +(290.371 - 502.937i) q^{74} +321.355 q^{76} +(209.365 + 362.631i) q^{79} +(83.5698 - 144.747i) q^{80} +(-168.000 - 290.985i) q^{82} -761.714 q^{83} -213.753 q^{85} +(7.62934 + 13.2144i) q^{86} +(-244.494 + 423.476i) q^{88} +(786.048 + 1361.48i) q^{89} +632.988 q^{92} +(-169.291 + 293.220i) q^{94} +(419.618 - 726.799i) q^{95} -1045.16 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 7 q^{5} - 32 q^{8} - 14 q^{10} + 25 q^{11} + 98 q^{13} - 32 q^{16} + 98 q^{17} - 119 q^{19} - 56 q^{20} + 100 q^{22} - 122 q^{23} + 129 q^{25} + 98 q^{26} + 146 q^{29} + 98 q^{31} + 64 q^{32} + 392 q^{34} - 289 q^{37} + 238 q^{38} - 56 q^{40} - 672 q^{41} + 614 q^{43} + 100 q^{44} + 244 q^{46} + 672 q^{47} + 516 q^{50} - 196 q^{52} + 375 q^{53} + 1526 q^{55} + 146 q^{58} + 763 q^{59} - 406 q^{61} + 392 q^{62} + 256 q^{64} + 654 q^{65} + 1041 q^{67} + 392 q^{68} + 3304 q^{71} - 189 q^{73} + 578 q^{74} + 952 q^{76} - 524 q^{79} + 112 q^{80} - 672 q^{82} - 574 q^{83} - 1244 q^{85} + 614 q^{86} - 200 q^{88} + 2394 q^{89} + 976 q^{92} - 1344 q^{94} + 706 q^{95} + 126 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 7 * q^5 - 32 * q^8 - 14 * q^10 + 25 * q^11 + 98 * q^13 - 32 * q^16 + 98 * q^17 - 119 * q^19 - 56 * q^20 + 100 * q^22 - 122 * q^23 + 129 * q^25 + 98 * q^26 + 146 * q^29 + 98 * q^31 + 64 * q^32 + 392 * q^34 - 289 * q^37 + 238 * q^38 - 56 * q^40 - 672 * q^41 + 614 * q^43 + 100 * q^44 + 244 * q^46 + 672 * q^47 + 516 * q^50 - 196 * q^52 + 375 * q^53 + 1526 * q^55 + 146 * q^58 + 763 * q^59 - 406 * q^61 + 392 * q^62 + 256 * q^64 + 654 * q^65 + 1041 * q^67 + 392 * q^68 + 3304 * q^71 - 189 * q^73 + 578 * q^74 + 952 * q^76 - 524 * q^79 + 112 * q^80 - 672 * q^82 - 574 * q^83 - 1244 * q^85 + 614 * q^86 - 200 * q^88 + 2394 * q^89 + 976 * q^92 - 1344 * q^94 + 706 * q^95 + 126 * q^97

Introduction

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